Flat bands in topological media

Abstract

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that in gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion -- the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.Comment: 9 pages, 5 figures, version to appear in JETP Letter

Structure of vortex-bound states in spin-singlet chiral superconductors

“…We choose τ to be of the order of two times the level spacing of the bound states ǫ 1 , Eq. (12). Figures 5 and 6 show the broadened LDOS for the two pairing symmetries.…”

“…The non-trivial topology gives rise to a multitude of interesting phenomena [1][2][3][4][5][6][7][8] , in particular subgap states in vortex cores and protected gapless edge modes that can carry quantized thermal current and particle current. Probably the most prominent example of a chiral superconductor is the spin-triplet (p x ± ip y )-wave state, which is believed to be realized in Sr 2 RuO 4 9,10 , in the A phase of superfluid 3 He [11][12][13] , and in two-dimensional cold atomic gases 14 . Spin-polarized (p x ± ip y )-wave superconductors support nondegenerate Majorana zero-energy modes localized at vortex cores [15][16][17][18][19][20] .…”

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

“…Flat-band ferromagnetism has been studied first by Lieb [16] and, subsequently, by Tasaki and Mielke [17][18][19][20]. More recently it has been shown that the high density of states of flat bands enhances the superconducting critical temperature [21,22]. Indeed, for fixed interaction strength, the flat-band dispersion provides the maximal critical temperature within mean-field BCS theory [23].…”

Flat bands with Berry curvature in multilayer graphene

“…Thus, the conduction band has a very flat pocket of a size p ∼ γ/v around the K and K points, and this pocket becomes perfectly flat in the limit N → ∞, corresponding to 'rhombohedral graphite'. The emergence of this flat pocket has previously been discussed in [23,24]. Now consider the application of a vertical electric field leading to potential difference V between any 2 consecutive layers.…”

“…On the top and bottom surfaces, there are undimerized lattice sites, which give rise to gapless surface states. The low energy single particle Hamiltonian for the surface states of an N layer graphene takes the form [23,24,26,27,30] …”